After Carlo died in GF1, was there one more hubby before we are introduced to Merle in GF2? When Mom states "you need to see your children first" when Connie comes to the table w/Merle in Reno, was she referring to the child she had w/Carlo, or the one with this second husband? Did she have another child this fictitious husband? Also, is the child she had w/Carlo portrayed by Andy Garcia in GF3?

We know that Connie had two sons by Carlo. She was pregnant with the first when Carlo beat her with his belt; and her second son was baptized on the day Michael "settled all family accounts." We know the second child's name was Michael Francis Rizzi (the baptism scene). In GFII we learn that the first son's name was Victor because Michael says to her, "You know that your oldest son Victor was picked up for some petty theft you know nothing about?" It's not clear that she had any kids by the second husband.
Vincent (Andy Garcia) is Sonny's illegitimate son by Lucy Mancini, the maid of honor at Connie's wedding.

thanks- who had custody of the two kids by Carlo- was it Michael?

Given the chiding tone Michael and Mama Corleone used on Connie at Anthony's party, it was she who had custody, although she seemed not to exercise it.

More likely than not she had some family retainer watching her kids during her "whore" period, and on Michael's dime no doubt.
Certainly they called Michael when Victor was picked up for some petty theft. She also did not live on the compound at that point.

Yeah, Mrs. Cicci.

"Retainer? Yeah, the family has lots of retainers".